I don’t think a woodwind player really learns the skill of “doubling” so much as he or she learns the skill of flute playing, plus the skill of saxophone playing, and so forth. 99% of being a good doubler is being a good flutist and a good saxophonist and whatever.

There are only a few aspects of woodwind doubling that are unique to multi-instrumentalists. These are:

The physical act of switching instruments. This becomes an issue in Broadway-type situations when instrument changes sometimes need to happen very quickly. It’s worth practicing these little bits of choreography until they can be done as quickly, quietly, and safely as possible. Tips: own good, sturdy stands, and keep your instruments laid out in a consistent way.

The mental effort of switching instruments. Years of developing a fine clarinet embouchure can go right out the window when making a quick change from tenor saxophone. The problem isn’t with your lips, it’s with your focus. As you switch instruments, shift gears mentally, too. Tips: warm up thoroughly on each instrument before the rehearsal or gig, and take a brief (sometimes very brief) moment of meditation as you physically change instruments, so that you are 100% in clarinetist mode by the time the reed hits your lip.

The guts to play an instrument that isn’t your best one. Even if your secondary instruments are quite strong, it can be unnerving to perform on one instrument when you know you can do better on a different one. Courage! You’ll be that much more experienced when the next gig rolls around. Tips: be aware of your body—is your nervousness affecting your posture? Breath support? Hand relaxation? If so, simply recognizing the physical symptoms can be enough to relieve them. Focus on musical things that you may be able to bring to the table despite technical deficiencies, like blend or phrasing.